A discontinuous free-surface flow analysis in open channels using FINITE DIFFERENCE and FINITE element methods is presented. Difficulties related to routing discontinuous flow, such as hydraulic jumps, back water flow and flow in junctions, produces very poor results when FINITE DIFFERENCE and classical Galerkin FINITE element methods are applied. A variance of FINITE element method, called Petrov Galerkin, uses discontinuous weighted test functions to dampen the numerically generated oscillations. Here one- dimensional linear elements were shown to estimate the flow depth and velocity accurately.

This paper investigates the reason behind the low magnetic field computation in cylindrical coordinates using FINITE DIFFERENCE method, when boundary conditions of the third or fourth kind are used. The same field computation has also been performed using the FINITE element method but this problem did not occur. It thus, presents a technique to overcome the problem of low magnetic field calculation using FINITE DIFFERENCE method. The results obtained by the new technique are in close agreement with the FINITE element method as well as the analytical solution. Finally, an analysis of the possible source of error in modeling magnetostatic boundary conditions in FINITE DIFFERENCE formulation of vector Poisson or Laplace equation in cylindrical coordinates is performed.

Drinking water demand is presently putting pressure on the City of Rey authorities. With a population of about one million in central Iran, the city relies on groundwater sources to tackle its growing need for the potable water. The quality of the groundwater, which currently contributes up to 50% to the total drinking water demand, has become a major concern. In this research, groundwater contamination in the Rey province and its social health impacts has been investigated. In particular, the problem of groundwater contamination caused by nitrates and bacteria due to anthropogenic activities in the area has been addressed. The study has been encountered with several difficulties such as shortage in proper field data and measurements, the vast study area as well as the complexity of nitrate fate. The main focus has been to identify the contaminant sources in the area, classify the saturated zones, learn about nitrate transport mechanisms and estimate the quantities finally discharged into the groundwater. The employed mathematical groundwater model shows that during a representative simulated 7 years dry period (from 1382 to 1388) the mean groundwater level will drop about 9.5 meters. In the eastern regions the water surface will move from -1.5 to -5 meter, while in the central regions the water surface will fall from -5 to -11 meters. In some areas in the western regions the water surface will even drop more than 22 meter. Groundwater quality model shows that the Rey aquifer consists of several overlying layers. It has been perceived that during the representative dry period, the nitrate concentration will increase in the central and eastern regions. Bearings of an under construction sewage collection network and treatment, however, has not been included in the current study. The new sewage system seems to have some impacts on the nitrate concentration in the Rey province and will put the actual figures lower than that that reported by the current study. The employed mathematical groundwater model (PMWIN) is competent to predict the groundwater potentials for periods of about 10 years. With conventional quality groundwater models, it is only possible to provide predictions up to 2 to 3 years. Which is why the errors of quality groundwater model would be increasingly, mount after 3 years.

Introduction: In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the FINITE DIFFERENCE method. One of the best subjects in the numerical analysis is a FINITE DIFFERENCE method (FDM). We used (FDM) to solve problems in mathematical physics, integral equations, and engineering, such as electromagnetic potential, fluid flow, radiation heats transfer, laminar boundary-layer theory and mass transport, Abel integral equations, and problem of mechanics or physics. Also in some physical problems such as fluid flow and heat transfer problems, the Laplace equations and the Poisson equations are describe by (FDM). In real life most phenomena are modelled by partial differential equations. Material and methods: First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results obtained here can be compared with the cubic B-spline method. Results and discussion: In addition, solving some examples demonstrates the validity and applicability of the approached method, so that the results are reported in the tables and their figures are shown. The high speed of the calculations, and the assurance of having an approximate solution are obtain by proving the stability of the method. Conclusion: The following conclusions were drawn from this research. Coefficients of the approximate function via Crank-Nicholson scheme are found very easily and therefore many calculations are reduced. The numerical results obtained here can be compared with the cubic B-spline method The assurance of having an approximate solution are obtain by proving the stability of the method.

Summary Urmia tunnel is being constructed to convey water to the Naghadeh and Urmia agricultural plains. About 1800 m of excavations are located in the alluvial ground. In this paper, a part of Urmia tunnel that is located in the alluvial ground was modeled using the numerical modeling FLAC3D and PLAXIS3D TUNNEL software packages. For this, first, the new Austrian tunneling method (NATM) was modeled. The NATM modeling results showed high displacement and instability of the face of the tunnel. Then, the earth pressure balance (EPB) machine was modeled and the face pressure was calculated. The modeling results showed suitable conformation between the two software packages. Moreover, a short-length part of the tunnel was excavated in the alluvial structure using the NATM, however, according to the modeling results, the face of the tunnel was unstable, and thus, the excavation was stopped. The face pressure, in the tunnel boring machine(TBM) was also calculated. Introduction Urmia tunnel is a challenging project because of its especial ground and excavation conditions. The main focus of this research is on tunneling in hard conditions like high groundwater level, high depth of tunnel, too much overburden, etc. An example of tunneling in hard conditions is the Urmia tunnel that is studied in this paper. The main objective of this paper is to select a suitable method of excavation in the tunnel. Methodology and Approaches In this study, the NATM and its combination with soil improvement methods, and also, the EPB machine were modeled using the numerical modeling FLAC3D and PLAXIS 3D TUNNEL software packages. A short-length part of the tunnel, which was excavated in the alluvial ground using the NATM, was considered in this study. Results and Conclusions The obtained modeling results in this study showed high displacement of both face and crown and instability of the face in the NATM modeling and combination of the NATM and soil improvement methods like jet-grouting and forepoling. Thus, the EPB machine was modeled and the face pressure was calculated.

A three-dimensional reactor static code for calculation of flux, power, multiplication FACTOR and also power peaking FACTOR in rectangular, triangular and cylindrical geometry core has been developed and benchmarked. For solution of the time independent neuron diffusion equation a FINITE DIFFERENCE method was used. To solve the equation with FINITE DIFFERENCE method, the speed of the applied numerical calculation is a major subject of interest, especially when the number of nodes increases. For this reason using an appropriate method to make the calculation faster is considered as the main priority. The aim of this paper is to present this three-dimensional nuclear reactor code with an emphasis made on the comparison between the advanced iterative algorithms in this code.